Eco 578 Assignment-1 due by Midnight (11:59pm) Monday, July 24th, 2017(Chapters 1, 2, 3, 4, 5, 6, and 7): Total 250 pointsTrue/False (Two points each)Chapter 11.An example of a Nominal scale variable is the make of a car.
2.An example of an ordinal variable is the driver’s license number of an individual.
3. Credit score is an example of a ratio scale variable.
4.Temperature is an example of an interval scalevariable.
5. The number of people eating at a busy local café between noon and 2:00 p.m. is an example of a discrete variable.
Chapter26.The relative frequency of a class is the frequency of the class divided by the number of classes.
7.A Histogram is a graphic that can be used to depict quantitative data.
8. The cumulative distribution function is initially increasing then decreasing.
Chapter 39.The Median is the measure of central tendency that divides a population or sample into two equal parts.
10. The median is said to be very sensitive to extreme values.
11.If there are 7 classes in a frequency distribution then the fourth class may not necessarily contain the median.
12.The sum of deviations from the mean must be zero.
Chapter 4
13. If events A and B are independent and A is not an impossible event, then P(A/B) is equal to zero.
14. If events A and B are mutually exclusive, then P(A/B) is equal to zero.
15. Events whose union has the probability equal to 1 are called Complementary events.
Chapter 516. If the probability of success is 0.2 and the number of trials in a binomial distribution is 100, then its standard deviation is 16.
17. If a fair coin is tossed 20 times then the probability of exactly 10 Tails is more than 17 percent.
18. The probability that a person catches a cold during the cold and flu season is 0.3. If 10 people are chosen at random, the sample variance for the number of persons catching cold is 1.45. (Hint: convert the problem to a binomial distribution problem).
Chapter 619.For a continuous distribution, P(X = 100) the same as P(X
20.If X is a continuous random variable then it is normally distributed.
21.The mean of a standard normal distribution is always equal to 0.
22. For a binomial probability experiment, if p is 0.1 and n is only 120, we can use the normal approximation to the binomial distribution without continuity correction.
Chapter 723.A sample size of 1000 is large enough to conclude that the sampling distribution of pis a normal distribution, if the estimate of the population proportion is .996.
24.The standard deviation of sample proportions increases as the sample size decreases.
25. If the population is normally distributed then the sample mean may or may not be normally distributed for small sample size.
Multiple Choices
(each question carries Four points):
Chapter 1
- Ratio variables have the following unique characteristic:
A.Meaningful order
B. Categorical in nature
C. Predictable
D.An inherently defined zero value
- Which of the following is (are) a categorical or Nominal variable(s)?
A. Daily Sales in a Store
B.Bank Account Balance
C.The Telephone number of a person
D.Air Temperature
E.Value of Company Stock
- Which of the following is (are) a quantitative variable(s)?
A.The make of a TV
B.The VIN of a car
C.The rank of a police officer
D.The Driver’s License Number of a person
E.The price of a TV
- The level of Satisfaction in a Consumer survey would represent a(n) ____________ level of measurement.
A.Nominative
B.Ordinal
C.Interval
D.Ratio
Chapter 25. A(n) ______ is a graph of a cumulative distribution.
A.Histogram
B.Bar Chart
C. Ogive
D.Pie Chart
6. When developing a frequency distribution, the class (group) intervals must be
A.Large
B.Small
C.Whole numbers
D.Mutually exclusive
E.Equal
7. If there are 120 values in a data set, how many classes should be created for a frequency histogram?
A.4
B.5
C.6
D.7
E.8
8. A company collected the ages from a random sample of its middle managers with the resulting frequency distribution shown below:
Class Interval Frequency
20 to 25 8
25 to 30 6
30 to 35 5
35 to 40 10
40 to 45 15
45 to 50 6
What would be the approximate shape of the relative frequency histogram?
A. Symmetrical
B.Uniform
C.Multiple peak
D.Skewed to the right
E.Skewed to the left
Chapter 39. In a statistic class, 10 scores were randomly selected with the following results were obtained (mean=71.5): 74, 73, 77, 77, 71, 68, 65, 77, 67, 66. What is the variance?
A.22.72
B.12.00
C.4.77
D.516.20
E.144.00
10. According to a survey of the top 10 employers in a major city in the Midwest, a worker spends an average of 413 minutes a day on the job. Suppose the standard deviation is 26.8 minutes and the time spent is approximately a normal distribution. What are the times that approximately 99.73% of all workers will fall?
A.[387.5 438.5]
B.[386.2 439.8]
C.[372.8 453.2]
D.[359.4 466.6]
E.[332.6 493.4]
11. If a population distribution is skewed to the left, then, given a random sample from that population, one would expect that the
A.Mean would be greater than the Median
B.Median would be greater than the Mean
C.Median would be equal to the mean
D.Cannot tell without looking at the Histogram
12. When using the Chebyshev's theorem to obtain the bounds for a 99.73 percent of the values in a population, the interval generally will be ___________ the interval obtained for the same percentage if normal distribution is assumed (empirical rule).
A.Shorter than
B.Wider than
C.The same as
D. A Subset of
13. In a hearing test, subjects estimate the loudness (in decibels) of sound and the results are:
68, 67, 70, 71, 67, 75, 69, 62, 80, 73, and 68. What is the median?
A.67
B.70
C.68
D.69
E.80
14. The numbers of rooms for 15 homes recently sold were: 8, 8, 8, 5, 9, 8, 7, 6, 6, 7, 7, 7, 7, 9, and 9. What is the standard deviation?
A.1.96
B.1.40
C.1.18
D. 16.00
E. 4.00
Chapter 415. If P(A) >0 and P(B) > 0 and events A and B are independent, then:
A.
P(A) = P(B)B.
P((
A|B)
) = P(A)C.
P(A
B) = 0D.
P(A
B) =P(A)/
P(B/A)E. Both A and C are correct
16. A recent marketing survey tried to relate a consumer’s awareness of a new marketing campaign with their rating of the product. Consumers rated their awareness as low, medium and high, and rated the product as Bad, Fair, or Good. The results are presented below:
Rating |
Awareness |
|
Low |
Medium |
High |
|
Bad |
0.10 |
0.15 |
0.07 |
Fair |
0.06 |
0.11 |
0.06 |
Good |
0.07 |
0.11 |
0.27 |
What is the probability that a consumer who is known to have ranked the product as fair had a high awareness of the ad campaign?
- 0.06
- 0.26
- 0.23
- 0.15
- 0.40
17. With the data in question 3 above, what is the probability that a randomly selected consumer either has a low awareness or rated the product poor?
A. 0.23
B. 0.32
C. 0.55
D. 0.45
E. 0.10
Chapter 518. In a study conducted by UCLA, it was found that 25% of college freshmen support increased military spending. If 6 college freshmen are randomly selected, find the probability that more than 3 support increased military spending
A.0.0376
B.0.1318
C.0.8682
D.0.9624
19. A fair die is rolled 10 times. What is the probability that an even number (2, 4 or 6) will occur 4 times or more?
A.0.1719
B.0.1172
C.0.6230
D.0.9453
E.0.8281
20. Which one of the following statements is not a necessary assumption of the binomial distribution?
A.Trials are independent of each other
B.The experiment consists of n identical trials
C.The probability of success remains constant from trial to trial
D. Sampling is with replacement
E.Each trial results in one of two mutually exclusive outcomes
21. In the most recent election, 20% of all eligible college students voted. If a random sample of 20 students were surveyed find the probability that less than five students voted in the election.
A.0.1746
B.0.2182
C. 0.3704
D.0.6296
Chapter 622.The area under the normal curve between z = 1 and z = 2 is ________________ the area under the normal curve between z = 0 and z = 1.
A. Greater than
B. Less than
C. Equal to
D.A, B or C above depending on the value of the mean
E.A, B or C above depending on the value of the standard deviation
23.If the wages of workers for a given company are normally distributed with a mean of $15 per hour, then the proportion of the workers earning more than $17 per hour
A.Is greater than the proportion of workers earning less than $17 per hour
B.Is greater than 50%
C.Is greater than the proportion of workers earning less than the mean wage $15
D.Is less than the proportion earning less than $17 per hour
E. Cannot tell without knowing the standard deviation
Chapter 724.A manufacturing company measures the weight of boxes before shipping them to the customers. If the box weights have a population mean and standard deviation of 90 lbs. and 24 lbs. respectively, then based on a sample size of 36 boxes, the probability that the average weight of the boxes will be more than 94 lbs. is:
A.34.13%
B.84.13%
C.15.87%
D.56.36%
E.16.87%
25.The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are delinquent more than 90 days overdue. The historical records of the company show that over the past 8 years 13 percent of the accounts are delinquent. For this quarter, the auditing staff randomly selected 250 customer accounts. What is the probability that less than 40 accounts will be classified as delinquent?
A.42.07%
B.92.07%
C.7.93%
D.40.15%
E.90.15%
Essay Type Questions (10 points each)
Chapter 21.
Consider the following data on distances traveled by people to visit the local amusement park.
Distance Frequency
1-8 miles 15
8-15 miles 14
15-22 miles 10
22-29 miles 8
29-36 miles 3
Expand and construct the table adding columns for relative frequency and cumulative relative frequency and construct the histogram of frequencies, plot the frequency polygon and the Ogive curve using Excel.
Chapter 32. The following frequency table summarizes the distances in miles of 100 patients from a regional hospital.
DistanceFrequency0-4 36
4-8 30
8-12 25
12-16 6
16-20 3
Calculate the sample variance and standard deviation for this data (since it is a case of grouped data- use group or class midpoints in the formula in place of X values, and first calculate the sample mean).
Chapter 43. At a college, 55 percent of the students are female and 35 percent of the students receive a grade of C. About 45 percent of the students are female and not C students. Use this contingency table.
Gender\Grade
|
C
|
Not C or
|
Female (F)
|
0.45
|
0.55
|
Male (M)
|
0.35
|
If a randomly selected student is male, what is the probability he is a “C” student?
4. The contingency table about customers of a store who buy cigars and/or beer is given below.
Beer |
No Beer |
Cigars |
0.10 |
No cigar |
0.15 |
0.50 |
|
Determine the probability that a customer will buy at least one of these items: cigar or beer.
- Four employees who work as drive-through attendees at a local fast food restaurant are being evaluated. As a part of quality improvement initiative and employee evaluation these workers were observed over three days. One of the statistics collected is the proportion of time employee forgets to include a napkin in the bag. Related information is given in the table.
Worker
|
Proportion of Dinners Packed
|
Proportion forgetting Napkin when packing Dinner
|
Joe
|
0.20
|
0.08
|
Jan
|
0.25
|
0.04
|
Cheryl
|
0.15
|
0.12
|
Clay
|
0.40
|
0.04
|
You just purchased a dinner and found that there is no napkin in your bag, what is the probability that Clay has prepared your order?
Chapter 56. In a study conducted for the State Department of Education, 30% of the teachers who left teaching did so because they were laid off. Assume that we randomly select 16 teachers who have recently left their profession. Find the probability that at least 7 of them were laid off.
7. A door-to-door sales person for a Household appliance has learned from her past experience that out of twenty-four demonstrations of her appliance only six demonstrations result in actual sales (long run average). This week she needs to make at least 5 sales. At least how many demonstrations does she need to perform to ensure that the probability of meeting her target is at least 95 percent? (
Read the chapter instruction posted by me to learn how to use Excel to find probabilities, and try to answer this question playing with cumulative probabilities-. You can also use Tables in the back of any Statistics book. Be careful about the wording of the question)
Chapter 68.If x is a binomial random variable where n = 100 and p = .1, find the probability that x is less than or equal to 14
using the normal approximation to the binomial.
9.The weight of a product is normally distributed with a standard deviation of 1.5 ounces. What should the average weight be if the production manager wants no more than 1% of the products to weigh more than 10 ounces?
Chapter 7
10.The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.0 inches and a standard deviation of 0.60 inches. A sample of 25 metal sheets is randomly selected from a batch. What is the probability that the average length of a sheet is between 30.03 and 30.30 inches long?